Determine Turán densities of uniform hypergraphs

Determine the Turán density 8pi(F)9 of every k-uniform hypergraph F for k at least 3.

Background

The paper introduces the classical Turán density of a k-uniform hypergraph and notes that determining its exact value is a major unresolved problem in extremal combinatorics. This broad problem concerns the asymptotic maximum edge density of k-uniform hypergraphs that avoid a prescribed forbidden hypergraph F.

References

Determining the value of~$\pi(F)$ for~$k$-graphs (with~$k\geq 3$) is one of the central open problems in combinatorics.

— Infinitely many accumulation points of codegree Turán densities  (2502.13485 - Li et al., 19 Feb 2025) in Introduction